Hume’s Dictum and Natural Modality: Counterfactuals

Hume’s Dictum and Natural Modality: Counterfactuals Jessica Wilson Department of Philosophy University of Toronto MoS ‘09 Nottingham

Hume’s Dictum • Hume’s version: • “There is no object, which implies the existence of any other if we consider these objects in themselves ...” (Treatise, Book I) • The rough contemporary version: • (HD): There are no metaphysically necessary connections between distinct entities. • The more precise contemporary version (see Wilson forthcoming): • (HD): There are no metaphysically necessary (conditional or unconditional) connections between wholly distinct, intrinsically typed entities.

HD’s influential role • Destructive applications: • Against necessitarian accounts of causal connections, properties and laws (Hume, Armstrong, Lewis) • Against certain theories of tropes (Armstrong) and truthmakers (Lewis) • Constructive applications: • Combinatorial accounts of modality (Armstrong, Lewis) • An explicit or inexplicit premise in lots of philosophical reasoning: • Concerning how to formulate physicalism (van Cleve, Kirk) • That various supervenience relations are equivalent (Sider, Bennett, Moyer) • That truthmaker theorists are commited to priority monism (Cameron)

Why believe HD: direct justification? • Contemporary proponents don’t accept Hume’s arguments for HD, so why believe it? • Some suggestions that HD is directly justified, as either analytic or as supported by intuitions we have no good reason to question. • But these suggestions don’t pan out (see Wilson forthcoming)

Why believe HD: indirect justification? • Might HD be rather indirectly justified, as an inference to the best explanation (IBE) of some phenomenon or other? • Schaffer (‘Quiddistic Knowledge’): • The best account of counterfactuals (CFs) requires HD.

The IBE from CFs for HD • [O]ne can formulate a direct argument for contingentism. For the best account of counterfactuals requires miracles (slight variations of the actual laws) in order to implement their antecedents [Lewis 1973: 75—7]. That is, to implement the antecedent that there are like charges at a given location (assuming this to be actually false), we need to imagine some miraculous swerving of say, two electrons, that brings them to said location. (Schaffer 2004, 216) • Note: talk of “miracles” is short for talk of goings-on at worlds with slightly different laws; strictly, no laws are violated at any world.

Assuming deterministic laws… • More precisely, Schaffer claims that contingentism is required if the laws are deterministic: • Assuming that the actual laws are deterministic […] such a miraculous swerving [of electrons] will require a slight violation of the actual laws. Hence the laws of the nearest possible world in which there are like charges here must be just slightly different from the actual laws. Thus to implement the counterfactual antecedent, one needs worlds with actual properties but alien laws. This is contingentism. (216) • So assume deterministic laws.

At best: motivation for HD (causal) • This IBE at best motivates HD (causal): HD as applied to the case of causal or other lawful connections between wholly distinct entities. • Still, HD (causal) is arguably the core application of HD.

Plan of the talk • Overview the account of CFs Schaffer has in mind. • Identify 3 sub-claims upon which Schaffer’s argument depends. • Assess each of the sub-claims. • Provide reasons for doubting two of the sub-claims.

CFs • CFs are subjunctive conditionals that may have false antecedents. • Where P and Q express the occurrence of certain goings-on, the associated CFs are schematically along lines of: • If it were (had been) that P, it would be (would have been) that Q. • For short: P>Q; ‘P would Q’

Similarity-based possible worlds accounts • The approach to CFs Schaffer has in mind (Stalnaker 1968, Lewis 1973) is a similarity-based possible worlds account. • Roughly (sufficient for present purposes), and treating the vacuous case: • P>Q iff (i) there are no possible P-worlds, or (ii) some P&Q world is comparatively more similar overall (“closer”) to the actual world than any P&-Q world

What does comparative overall similarity (COS) come to? • An adequate account of COS should allow for any two possible worlds to be ordered, and (perhaps) ensure that the actual world is more similar overall to itself than any other possible world. But that leaves a lot open. • The approach to COS that Schaffer has in mind is along lines discussed in Counterfactuals (1973, 75--7) and developed in ‘Counterfactual Dependence and Time’s Arrow’ (1979).

The main constraint on Lewis’s account: CF asymmetry • Lewis’s account is primarily motivated by what he takes to be “the asymmetry of counterfactual dependence” (CF asymmetry, for short): • The way the future is depends counterfactually on the way the present is. If the present were different, the future would be different; […] Not so in reverse. Seldom, if ever, can we find a clearly true counterfactual about how the past would be different if the present were somehow different. (32)

The 4-fold way • Lewis offers the following 4-fold weighting of respects of similarity as constituting an account of COS satisfying CF asymmetry: • (1) It is of the first importance to avoid big, widespread, diverse violations of law • (2) It is of the second importance to maximize S/T region of perfect match of particular fact • (3) It is of the third importance to avoid even small, localized, simple violations of law • (4) It is of little or no importance to secure approximate similarity of particular fact

Case study: the Nixon CF • The Nixon CF: • If Nixon had pressed the button, a holocaust would have ensued. • First, what is the antecedent past like in the closest P-worlds? • Only a small violation of law (say, a few differently firing neurons) is needed for Nixon to press the button. Here we gain exact S/T match of antecedent and actual past (prior to the transition period) at the cost of only a small miracle. • P-worlds brought about by evolving different initial conditions forward fail to preserve exact S/T match of antecedent and actual past, hence are farther away than “miracle” P-worlds.

The Nixon CF, stage 2 • Second, what is the antecedent future like in the closest P-worlds? • Might the closest P-worlds be ones where another small miracle “undoes” the button-pushing so that antecedent and actual futures are S/T exactly alike? No: according to Lewis there are no such worlds: undoing all the traces of the button-pushing takes a multitude of miracles, adding up to a big violation of law. • Since it’s more important to avoid such large scale violations than togain exact S/T match, the closest worlds are holocaust worlds, after all.

A “COSMic” account • Generalizing, Lewis suggests that his account of COS accommodates CF asymmetry (modulo the transition period needed to smoothly implement the antecedent) in all but a few “non-standard” contexts. • Call an account of COS that aims to preserve CF asymmetry along Lewisian lines a “COSMic” account (a Miracle-based account of Comparative Overall Similarity).

A few words about context… • Lewis takes the “standard” context of CF evaluation to presuppose a COSMic account. • Schaffer doesn’t need anything this strong for his IBE. He just needs there to be at least one context, relevant to evaluating the non-vacuous truth of an appropriately wide range of CFs, that plausibly presupposes a COSMic account. • On the other hand, if the IBE from CFs to HD is to have independent traction, the context at issue can’t be jury-rigged or artificial: • Let’s assume an account of similarity as per a COSMic account. Now consider the CF…

Assessing Schaffer’s argument:3 sub-claims • We are now in position to assess Schaffer’s claim that the best account of CFs (that is, Lewis’s) supports HD (causal). • Schaffer’s claim depends on three sub-claims: • (1) The best account of CFs is a similarity-based account • (2) For some non-artificial context, the similarity-based evaluation of an appropriate range of CFs involves appeal to a COSMic account • (3) A similarity-based account of CFs, filled in with a COSMic account, requires the truth of HD (causal).

Assessing (1):Why a similarity-based account of CFs? • Similarity-based possible-worlds accounts of CFs are hegemonic. • Plus, the main competitors to possible worlds accounts… • Allowing that CFs with impossible antecedents may be non-vacuously true (Nolan 1997, Kment 2006) • Variations on the “strict conditional” approach (Lowe 1995, von Fintel, 2001, Gillies 2007) • …are also similarity-based accounts, in taking the proper evaluation of CFs to require attention to goings-on in (some range of) relevantly similar (to the actual world) worlds satisfying the antecedent. • So grant (1).

Assessing (2):Why a COSMic account? • Given that the best account of CFs is a similarity-based account, should we moreover suppose that there is some non-artificial context in which the evaluation of an appropriate range of CFs involves appeal to a COSMic account?

The main advantage:preserving CF asymmetry • Schaffer takes a main advantage of a COSMic account that it allows implementation of the CF antecedent without complete backtracking: • “The necessitarian […] may attempt to implement the counterfactual antecedent without miracles, by tinkering with the initial conditions instead, in such a way as that the actual laws will evolve into the antecedent. But this introduces complete ‘backtracking’, yielding implausible counterfactual dependencies of the initial conditions on the present charges.” • Hence Schaffer follows Lewis in thinking that some non-artificial contexts of CF evaluation presuppose CF asymmetry.

So, why (contexts presupposing…) CF asymmetry? • So let’s consider the motivations for there being contexts presupposing CF asymmetry, as motivating a COSMic account.

Some terminology: “forward-” and “backward-facing” CFs • Let a “forward-facing” CF be one where the consequent of the CF is in the antecedent future. • Let a “backward-facing” CF be one where the consequent of the CF is in the antecedent past.

Motivations for CF asymmetry • Lewis’s main reasons for thinking that there are such contexts are: • 1. Ordinary reasoning about CFs presupposes CF asymmetry. • 2. Backwards-facing reasoning/CFs are typically false or indeterminate. • Schaffer offers a couple of other reasons. • Lewis also cites indirect reasons, associated with CF asymmetry explaining the asymmetries of causation and of openness. I don’t think these are compelling, but won’t focus on them here.

Motivation (1) for CF asymmetry: ordinary reasoning • Lewis: • [I]n reasoning from a counterfactual supposition about any time, we ordinarily assume that facts about earlier times are counterfactually independent of the supposition and so may freely be used as auxiliary premises. (33) • Often, indeed, we seem to reason in a way that takes it for granted that the past is counterfactually independent of the present … (33) • Consider, e.g., the Jim/Jack case: • Given that Jim and Jack had a fight yesterday, we may suppose that it is true that if Jim were to ask Jack for help today, he would say no; for (given that the fight occurred) Jack is still mad at Jim, and so isn’t inclined to help Jim.

Ordinary reasoning about forward-facing CFs doesn’t require asymmetry • Let’s first consider ordinary reasoning about forward-facing CFs. • Grant that evaluation of forward facing CFs typically holds fixed some aspects of the antecedent past. • Still, this doesn’t show that such evaluation presupposes anything as strong as CF asymmetry. • At best such cases show that ordinary reasoning typically holds some aspects of the past fixed (e.g., the fight, in the Jim/Jack case).

Ordinary reasoning about antecedent implementation rejects CF asymmetry • If you ask an ordinary reasoner how a CF antecedent would be implemented, they will (so I claim) attempt to tell a story maximizing plausibility, probability, and/or comprehensibility. • If Jim were to ask Jack for help today notwithstanding their having fought yesterday, Jim would have earlier gotten into some fairly serious trouble; he would have weighed his options, decided to swallow his pride and ask Jack for help; etc. • Ordinary reasoning does not assume or attempt to maximize counterfactual independence of antecedent past, as CF asymmetry supposes.

Ordinary reasoning about antecedent implementationrejects a COSMic account • Relatedly, it is unclear that miraculous implementation of antecedents is ever presupposed in ordinary reasoning about forward-facing CFs: • “It is true that often enough when we say,`If A had been, then C would have been’ for actually false A, we do not much worry abut how A would or could have come about. But it is never acceptable for serious purposes to say ‘If A had been, then the actual necessitating causes of not-A would all still have occurred but there would have been a miracle, so …” (Hiddleston 2001, 62). • At least, that’s true of CFs with lawful antecedents. Reasoning about CFs with unlawful antecedents (“If I had miraculously disappeared, the car wouldn’t have hit me”) is besides the point of independently motivating HD (causal).

Ordinary reasoning about backward-facing CFs rejects CF asymmetry • Much ordinary counterfactual reasoning involves evaluating backwards-facing CFs: • If the pilot had not pressed the button, she would have previously gotten different orders. • If my client had punched the claimant, he would have survived his childhood with both arms intact. • Backward-facing reasoning/CFs obviously do not presuppose CF asymmetry.

Summing up: ordinary reasoning does not support a COSMic account • The main virtue of a COSMic account is that it accommodates contexts presupposing CF asymmetry. • Lewis claimed that ordinary reasoning provided such a context. • But it doesn’t. • So ordinary reasoning doesn’t support a COSMic account.

Schaffer’s suggested context #1 • Schaffer (p.c.) suggests two special contexts where CF asymmetry might be presupposed. • Context 1. There seem to be some contexts in which we want to judge false claims like "had I raised my hand in Caspar Hare's Bellingham talk, the initial conditions of the cosmos would have been different" (assume a deterministic world in which I did not actually raise my hand). • Response: a context in which such a claim might be considered false under the assumption of deterministic laws would seem to be one assuming either that such actions are truly free (i.e., non-nomological) and so outside of the causal nexus, or that a COSMic account is correct. Neither context is relevant to showing that there is a non-artificial context where CF reasoning about nomological goings-on presupposes a COSMic account.

Schaffer’s context 2 • Context 2: We often take counterfactual dependencies to be at least indicative of (if not constitutive of) causal relations, and so we often want to deny claims like “if the bottle had not shattered, then Suzy would not have thrown the rock”. • Since the denial of CF asymmetry is compatible with holding some aspects of the past fixed (e.g., Suzy’s throwing), that there are contexts where the Suzy CF is false doesn’t itself motivate a COSMic account. • Indeed, the falsity of the Suzy CF would plausibly advert either to past-changing facts (placement of bubble wrap), a different throw, or goings-on occurring after Suzy’s throw (moving of bottle). • Certainly it unclear there is any non-artificial context where the falsity of the Suzy CF presupposes that Suzy accurately throws a rock at the unprotected bottle, but a miracle prevents the shattering.

Motivation (2) for CF asymmetry:backward-facing reasonings/CFs are false/indeterminate • Lewis suggests that contexts not presupposing CF asymmetry are problematic: • “[A] counterfactual about how the past would be different if the present were somehow different […] unless clearly false, normally is not clear one way or the other.” (Lewis, 32) • “Today I am typing words on a page. Suppose today were different. Suppose I were typing different words. Then plainly tomorrow would be different also; for instance, different words would appear on the page. Would yesterday also be different? If so, how? […] I do not think there is anything you can say about how yesterday would be that will seem clearly and uncontroversially true.” (32) • How about “If I were typing different words today, I would not have been in a fatal accident yesterday”?

Epistemological concern 1: initial condition-based indeterminacy • But perhaps CF asymmetry is generally required for truth or determinacy? • Lewis: too much backtracking “would make counterfactuals useless; we know far too little to figure out which of them are true under a resolution of vagueness that validates very much backtracking.” • Bennett: • “We must excuse ourselves from unlimited backtracking if we are to have good grounds for believing any counterfactuals. [This holds] if our world is governed by fairly deterministic laws, for then almost any antecedent will imply an earlier difference which will imply a still earlier one which …and so on back for a million years, say, and then forward along other branches of the downward-spreading causal tree. Of course we cannot do this, but that is my point: because we cannot do it, we adopt standards which don’t require us to do it” (391)

Is initial condition-based indeterminacy really a problem? • The concern here seems to be that tweaking of initial conditions in order to implement of the antecedent will necessarily bring about so many other differences from the actual world that we wouldn’t be able to know what the present state of a deterministically implemented antecedent world was, much less evaluate what would happen in the future at such a world. • But it is unclear that this is so.

Complete backtracking may be compatible with broad similarity • If the laws are deterministic, then every state of the world entails every other. So to deterministically implement a CF antecedent, antecedent and actual pasts cannot share any world-states. • But perhaps difference in world-states is compatible with antecedent and actual pasts being very, or at least, relevantly similar. • The suggestion is that variation from the actual past needed to implement the antecedent can be “contained”, such that corresponding states could be very similar (indeed, perhaps exactly alike) outside the region of difference. • Yet more weakly: it suffices to answer the Lewis/Bennett concern that states of the antecedent past are very similar in any respects (e.g., the fight, human evolution) relevant to evaluating the CF.

Pourquoi pas? • So, can counterfactual antecedents be deterministically implemented compatible with broad similarity of world-states? • My expert says: • I think the answer is: no one really knows, it's just too hard a dynamical question. But I also think by the standards that usually govern such things, you'd be within your rights to say that such solutions exist. People often assume that realistic deterministic dynamics would permit that sort of variation. Let someone else try to show why it *couldn't* happen! • In the background here is the fact that macro-phenomena of the sort typically relevant to CF evaluation are compatible with a vast range of micro-states (think of macro statistical mechanical phenomena), making room for all kinds of interesting “micro-conspiracies” that would preserve macro (that is, approximate) similarity.

Non-exact match… • To be sure, the resulting world wouldn’t exactly match the actual world in respect of past (micro) S/T matters of fact. • This would go against an aspect of a COSMic account. • But we are here considering whether there are any contexts where we must accept a COSMic account. • The more general moral is that Lewis and Bennett’s epistemological concern about initial condition backtracking can be addressed without accepting a COSMic account.

Epistemological concern #2:underspecification • Consider the CF: • If the pilot had not pushed the button, she would have received different orders. • Couldn’t any number of histories have led to the button’s not being pushed---some involving different orders from on high, some not? • If so, then it would be natural to see the CF either as indeterminate or false.

Forward-facing CFs face the same problem • To start, note that there is no concern here that doesn’t also attach to forward-facing CFs. Consider: • ‘If I were to drop the sugar cube in water, it would dissolve’. • One might also argue that this CF is false or indeterminate, for similar reasons as in the case of the pilot CF: • There are any number of circumstances in which I might drop the sugar cube in water. In some of these, the cube dissolves; but in others, it doesn’t (e.g., because the disposition is masked somehow).

The same problem… • Indeed, Hajek takes such considerations indicate that most CFs are false: • I were to let go of the cup, it would fall. And if it were to fall and hit the floor, it would break.” Well, no, and no—it might not, and it might not. If I were to let go of the cup, a sudden gust of wind might lift it higher; and if it were to fall and hit the floor, another gust of wind might slow down its fall sufficiently to spare it a damaging impact. Quantum mechanics is just a handy, coverall way for me to secure the truth of a huge raft of undermining ‘might’ counterfactuals in one fell swoop. But other anomalous happenings could do the job just as well on a case by case basis. (p. 10)

CFs and background conditions • I’m not quite so pessimistic. • Perhaps strategies for accommodating the determinate truth of disposition ascriptions by appeal to typical or context-relative background conditions will work for backwards-facing CFs: typically, or in certain contexts, pilots do what they’re ordered to do. • In any case, if there’s no problem in evaluating forward-facing CFs against such background conditions, why is there any problem in evaluating backward-facing CFs against such conditions? • And if there is a problem in both cases, then Schaffer’s IBE from CFs for HD won’t get off the ground.

Summing up: OK to deny (2) • None of the stated reasons for there being non-artificial contexts presupposing CF asymmetry, hence a COSMic account, go through. • Hence Schaffer’s claim that… • to implement the antecedent that there are like charges at a given location (assuming this to be actually false), we need to imagine some miraculous swerving of, say, two electrons, that brings them to said location (216) • …is incorrect.

Assessing (3):Does a COSMic account support HD (causal)? • Suppose we accept a similarity-based account of CFs along with a COSMic account of COS. • Are we thereby committed to the truth of HD (causal)? • Perhaps not.

Property counterpart theory (PCT)? • Suppose that you reject HD (causal); you think (like Shoemaker and others) that any world where, e.g., mass exists is a world where the laws are the same as the ones that actually govern mass. • You might nonetheless (try to) implement a Lewisian account of CFs by taking miracle worlds to be ones where the entities at issue are not identical to, but rather just relevantly similar to, the actual entities at issue. • “Miracle” worlds involve shmass, not mass. • That is, endorse PCT (see Heller, ‘Property Counterparts in Ersatz Worlds’ 1998).

Objection: you still get HD (causal) • What it is for ‘Humphrey could have won the election’ to be true is for Humphrey to have the de re modal property of possibly winning. • What makes it the case that Humphrey has this modal property is that he has a counterpart that does win. But in any case, Humphrey himself has the modal property. • Similarly, even if what makes it the case that mass has this property is that mass has a counterpart entering into different laws, it still is the case that mass has the de re modal property of being such as to be possibly governed by different laws.

Response: having the de re property isn’t enough to verify HD (causal) • Recall the metaphysical claim in HD (causal): (tokens of) entities of the same type that actually exist might exist and be governed by different laws. • PCT doesn’t entail this claim. • PCT only requires that properties relevantly similar to the property P having the de re modal property might exist and be governed by different laws.

Compare Stalnaker’s discussion of Lewis’s CP theory • Lewis’s CP theory does not entail that I could exist in a different world and be giving a different talk. • Lewis is “anti-essentialist” only in denying that there is “a discriminatory distinction” between two ways that a thing may be related to its properties: • An essential property is a property that a thing has in all possible worlds in which it exists. An accidental property is a property that a thing has in the actual world, but lacks in some other world. […] According to Lewis’s theory, individuals have counterparts---things that resemble more than anything else---in other worlds, but each individual itself exists in only one possible world. Hence no individual can have accidental properties in the sense defined above: properties that it lacks in some other possible world. (Stalnaker 1979, 72) • A PCTist needn’t take properties to be world-bound, but the same moral applies.

Question: what is the fixed base for the CP relation? • Counterparthood for particulars is typically determined by similarity with respect to a fixed base of properties. How are we supposed to compare properties themselves for similarity? • Some possibilities… • Compare S/T pattern of distribution of properties (Heller’s strategy) • Compare nomological roles • These strategies might require trans-world identity of some properties or particulars, but that needn’t kill the account (compare resemblance-based accounts of properties).

Hume’s Dictum and Natural Modality: Counterfactuals